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On Regularity for Constrained Extremum Problems. Part 1: Sufficient Optimality Conditions

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Abstract

The main aspect of the paper consists in the application of a particular theorem of separation between two sets to the image associated with a constrained extremum problem. In the image space, the two sets are a convex cone, which depends on the constraints (equalities or inequalities) of the given problem, and its image. In this way, a condition for the existence of a regular saddle point (i.e., a sufficient optimality condition) is obtained. This regularity condition is compared with those existing in the literature.

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Authors and Affiliations

  1. Faculty of Sciences (Mathematics), University of Pisa, Largo B. Pontecorvo 5, 56127, Pisa, Italy

    A. Moldovan

  2. Faculty of Sciences (Mathematics) and Faculty of Economics, University of Verona, Viale Università, Palazzina 32, 37129, Verona, Italy

    L. Pellegrini

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  1. A. Moldovan
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  2. L. Pellegrini
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Correspondence to L. Pellegrini.

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Communicated by F. Giannessi.

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Moldovan, A., Pellegrini, L. On Regularity for Constrained Extremum Problems. Part 1: Sufficient Optimality Conditions. J Optim Theory Appl 142, 147–163 (2009). https://doi.org/10.1007/s10957-009-9518-3

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  • DOI: https://doi.org/10.1007/s10957-009-9518-3

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